Answer:
The length of the mosquito in the picture is 117.6 mm.
Step-by-step explanation:
This question can be solved using a rule of three.
The real size of the mosquito is 16 mm, which is 100% = 1.
In the picture, the size is magnified 635%, so it is 100+635 = 735% = 7.35. So
16mm - 1
x mm - 7.35
x = 7.35*16 = 117.6
The length of the mosquito in the picture is 117.6 mm.
Answer:
The value of h'(7) = 44 .
Step-by-step explanation:
Given:
f'(7)=9 and g(7)= 5
We have to find : h'(7)
Also,
⇔ 
...equation (i)
Plugging the value of 'x' = 7 in equation (i) the equation can be re-framed as:
⇔ 
⇔
Now plugging the value of f'=(7)=9 and g(7)=5 in the above equation:
⇔ 
⇔ 
⇔ 
So the value of h=(7) = 44 .
Answers
Surface area is 964 cm2
Volume is 1872 cm3
Step by step
Using L=length, w=width, h= height
Surface area is found by adding the area of all 6 sides. Area is found by multiplying L x W.
8x18 = 144 x2 sides = 288
18x13 = 234 x2 sides = 468
8x13 = 104 x2 sides = 208
Total all sides = 964
Volume of a rectangle is found by multiplying L x W x H
13 x 18 x 8
Volume is 1872 cm3
Let's say Ralph can do the chores in h hours, and Jo in 2h. Then:
1/h+1/2h=1/6
6+3=h
h=9
Ralph takes 9 hours working alone; Jo takes 18 hours
☺☺☺☺
<span>Part I: Determining Dimensions
Arnold
has been given a 6 foot by 6 foot sheet of cardboard to make an open
box by cutting an equal size square from each corner, folding up the
resulting flaps, and taping at the corners. Your task is to label
dimensions on a sketch with the same size variable cut from each corner.
*You don't have to draw one, just explain what it would look like*
Answer:
Base of the box:
it is a square
side of the base = 6 foot - x - x. = 6 - 2x
Height of the box: x
Part II: Analyze
How does each variable expression relate to the length, width, and height of the box when folded?
Answer:
length = width = 6 - 2x
height = x
Part III: Extend your Findings
a. Based upon the variables you used in Part II, write a product for the volume.
Answer:
Volume = area of the base × height
Volume = (6 - 2x)² x
b. Expand the product to write a volume function.
Answer:
Volume = (36 - 24x + 4x²)x
Volume = 36x - 24x² + 4x³
c. What domain makes sense for the volume?
Answer:
Since x is a physical dimension x is greater than 0
Since the lenght of the cardboarc sheet is 6 and two squares are cut off, x has to be less than 3
So, the domain is (0, 3)
d. Guess and check values to find the size cut that produces a maximum volume.
*Six guesses are required*
Answer:
x </span>Volume = 36x - 24x² + 4x³
0.1 36(0.1) - 24(0.1)² + 4(0.1)³ = 3.36
0.5 36(0.5) - 24(0.5)² + 4(0.5)³ = 12.5
1.0 36 - 24 + 4 = 16
1.5 36(1.5) - 24(1.5)² + 4(1.5)³ = 13.5
2.0 36(2) - 24(2)² + 4(2)³ = 8
1.7 36(1.7) - 24(1.7)² + 4 (1.7)³ = 11.49
1.2 36(1.2) - 24(1.2)² + 4(1.2)³ = 15.55
Then you can guess that the maximum volume is pretty close to 16 and it is whenx is close to 1.
2.9
